Letter To Scientific American ----------------------------- Concerning "The Fairest Vote of All" by Dasgupta & Maskin (March 2004). A simpler and better voting system is "range voting" where each voter provides as his vote, a score for every candidate on a 0-10 scale. The candidate with the highest summed score wins. My 2000 paper "Range voting" (available as #56 at www.math.temple.edu/~wds/homepage/works.html; see also #59) studies it heavily and compares it with numerous other proposed voting systems by means of millions of computerized simulated elections. That study clearly showed the superiority of range voting over all other yet-proposed systems, as measured by a yardstick called "Bayesian regret". Dasgupta & Maskin do not actually specify the voting system they are pushing (!), but I believe that they meant "Black's system," which dates to the 1950s or earlier. It was described in my paper and included in my computerized study. Dasgupta & Maskin completely ignored the massive effects of voters who vote "strategically" instead of honestly in an attempt to "game the system." For example, in the 2000 election, many voters who liked Nader best, instead chose to dishonestly vote (as they were urged in hundreds of editorials) for Gore, for strategic reasons ("don't waste your vote"). My paper's theorem 8 shows that with strategic voters, the winner in an N-candidate Black-Dasgupta-Maskin election will be exactly the same as the winner in a plain-plurality election! This theorem destroys Dasgupta & Maskin's claim that Black's system is superior to plain plurality. This theorem also holds for the "IRV system" (which Dasgupta & Maskin also mention but do not describe, but which also is described and studied in my paper). This is an equally severe indictment of IRV. My computerized studies allowed either honest or strategic voters, and allowed adjustable "voter ignorance," and included many different "utility generators" for creating different election scenarios. In all, 432 different kinds of scenarios were investigated, running millions of elections for each. Range voting performed as well or better than every competing system in every scenario - very conclusive! Not only are IRV and Black inferior to range voting on performance grounds, they also are harder to describe and use and are more susceptible to near-ties such as Bush-Gore 2000 (since ties can occur at more than one stage in those procedures). Dasgupta & Maskin also disserve us by propagating the myth that the "true majority winner" (if one exists) is the best. Counterexample: Suppose candidate Hitler, if elected, will award 51% of the voters 1 dollar worth of societal benefit but kill the other 49%. Meanwhile candidate Gandhi will award 49% of the voters 1000 dollars and kill nobody. Everybody knows this and everybody acts for their own benefit solely. While Hitler will be the "true majority winner," Gandhi is better for society as a whole. Range voting with honest voters would allow the election of Gandhi in this situation, but no other competing system would. In conclusion, I point out that the "Bayesian regret" yardstick is a QUANTITATIVE way to compare voting systems. It allows estimating the damage society suffers from poor voting system performance to be translated into extremely real terms such as dollars. So here are 3 systems: (1) choose the winner at random (essentially like monarchy, but probably worse). (2) Use plurality voting (essentially what happens in most contemporary democracies). (3) Use range voting. My study shows that the societal benefit obtainable by switching from (2) to (3) EXCEEDS that obtained from switching from (1) to (2), regardless of whether the voters are honest or strategic. The damage society is suffering by employing the flawed plurality voting system thus is absolutely immense, outrageous, and inexecusable. --Warren D. Smith. ------------------------------------------------------------------- POSTSCRIPT: Dasgupta and Maskin in their more formal paper On the Robustness of Majority Rule and Unanimity Rule http://www.econ.cam.ac.uk/faculty/dasgupta/ rely heavily on a crude model (due to Duncan Black) of voters as 1-dimensional single-peaked distributions. In this model (Black proved, and Dasgupta and Maskin re-proved in more generality) we have the THEOREM that "preference cycles" are impossible. That theorem's validity is due to the fact that, if 3 candidates A,B,C occur in that order along the 1-dimensional line, then (in Black's model) no voter can regard B as worse than both A and C. However, this model is unrealistic (and hence cycles can and will occur in reality) for several reasons: 1. Real voters are stategic. A voter may well decide to exaggerate the badness of B, dishonestly ranking him "worst", for strategic reasons ("don't want to waste my vote"). 2. Real voters CAN and SHOULD rank B as worse than both A and C. For example, suppose the most important issue is whether to invade and conquer an enemy country that is threatening to kill us all by next week, or to make a peace treaty with them. Well, I would pretty much prefer my leader to do one or do the other, but definitely do it fast. I would NOT want my leader to take the middle course and do neither. 3. Real voters are not 1-dimensional. For example, consider the Gore-Bush-Nader 2000 election. Voter #1 cares about honesty and says that, as far as honesty is concerned, Nader>>Gore>Bush. Voter #2 cares about experience: number of years in high office. So he ranks Gore>Bush>>Nader. Voter #3 cares about lowering his taxes and figures Nader, as a consumer advocate, will cut taxes more (or raise them less) than Gore, so he ranks Bush>Nader>Gore. The net result of these 3 voters is to create a preference cycle. The net result of this is that the Dasgupta-Maskin paper has little connection to reality. Their paper seems to have a pretty nice theorem in it - albeit one whose precise statement is rather hard to elucidate - but it is a theorem that lives in a mathematical fantasy world, not the real world. END OF POSTSCRIPT.